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The effects of angular orientation on flame spread over thin materials
Fire Safety Journal 36 (2001) 291}312
The e!ects of angular orientation on #ame spread over thin materials James G. Quintiere* Department of Fire Protection Engineering, University of Maryland, Building 88, College Park, MD 20742, USA Received 5 April 2000; received in revised form 16 August 2000; accepted 13 September 2000
Abstract Data were taken to show the #ame spread characteristics of thin materials burning on an insulating substrate. Metalized polyethylene terephthalate (0.20 mm) and paper (0.17 mm) were burned on the surface of glass "ber insulation. Flame spread was measured in the upward or downward facing orientation for the material and in the directions of gravity assistance (up) or gravity opposition (down). Measurements were taken at various angles ranging from a vertical to a horizontal orientation. A theoretical analysis was developed to predict the #ame spread as a function of material properties, sample orientation, and #ame spread direction. The onedimensional theory was in reasonable agreement with the paper data. Vertical upward spread was found to yield the highest velocity. Critical angles (measured from the vertical) show transition to increasing #ame spread for downward bottom spread at !603, and for upward top surface spread at 603. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Flame spread; Thin materials; Direction; Inclination; Angle
1. Introduction This study was motivated by the need to investigate the #ammability of aircraft thermal}acoustical insulation blankets. In particular, it considers the thin "lm which encapsulates the insulation material. Blankets of this insulation lines the interior skin of aircraft cabins to reduce the noise and heat transfer. Two small-scale #ame spread tests apply to thermal}acoustical insulation blankets. The "rst is a regulatory requirement contained in FAR 25.853, a vertical Bunsen burner test. The second is an industry standard called the `cotton swab testa, which * Corresponding author. Tel.: #1-301-405-3993; fax: #1-301-405-9383. E-mail address: [email protected] (J.G. Quintiere). 0379-7112/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 0 ) 0 0 0 5 1 - 5
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Fig. 1. Flame spread on a metalized pet-"berglass insulation "lm after ignition by an electrical arc.
consists of ignition by alcohol-soaked cotton swabs inserted in the center of a horizontal sample and at the crease it makes with a vertical section [1]. Attempts to simulate realistic ignition sources were conducted by Cahill [2]. One example, of upward and downward spread on a metalized polyethylene terephthalate (PET) "lm insulation blanket is shown in Fig. 1 on a curved aircraft cabin section. The maximum upward burnout region (U ), downward pyrolysis region (D ), and upward #ame length (L ) were measured from a video recording of the test. Despite erratic burn fronts with discontinuous #aming regions, the maximum speeds and #ame lengths appear approximately constant at speeds of 5.9 mm/s up, 2.6 mm/s down, and lengths of 120 mm for the upward #ames. It was generally found that the ignition and sustained #ame spread of typical aircraft insulation blanket "lms were di$cult to achieve by small #ame sources. Some speculated that Bunsen burner type testing for samples oriented downward and 453 with the vertical gave more consistent spread. As a consequence, it was decided to investigate the e!ect of orientation and inclination angle on the #ame spread of thin "lms. A metalized PET "lm, which seemed easily ignitable by a small #ame, was selected as a representative aircraft material. Later it was found that a thin-paper specimen gave more consistent one-dimensional #ame spread results. Both upward and downward #ame spread were examined.
2. Experimental arrangement The experimental test apparatus consisted of a steel holder that could sandwich a test sample "lm against "berglass insulation without compression. The apparatus is shown in Fig. 2. A grid was inscribed at 0.5-in. (1.27-cm) increments on each outward facing steel longitudinal edge. This enabled an observer to identify the #ame position.
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Fig. 2. Flame spread apparatus.
A digital clock was positioned so that the time and #ame position could be simultaneously viewed on a video recording. For burning on the underside of the sample, a mirror was positioned to observe the clock and the #ame progression. A rod attached to one face of the steel holder and a clamp arrangement allowed the assembly to be rotated. A level gage and protractor was used to set the angle, , to the vertical. A small butane di!usion #ame approximately 1}2 cm in length and 1 cm in diameter was used to ignite the "lm sample. Once ignition occurred, the igniter was withdrawn. If #ame spread terminated before the end of the 12-in. (30.5-cm) sample length, the igniter was reapplied. This was repeated as necessary. Two samples were tested. The "rst was representative of aircraft thermal}acoustical "lms; the second was a brown paper towel (napkin) commonly found in dispensers for drying hands. The latter was selected because the metalized polyethylene terephthalate (PET) did not always sustain #ame spread, and a more consistent material was desired. It was found that the paper napkin did yield similar results to the PET, and it also had similar properties. Component material properties are shown in Table 1. The samples were tested over angles ranging from 903 (vertical) to 03 (horizontal). A designation of `#a represents an upward facing sample (top) and `!a a downward facing sample (bottom). Both upward and downward spread were examined. Figs. 3a}g display the progression of the #ame tip position as a function of time for the paper napkin. Note that the time-scale zero point was arbitrarily selected, and ignition was started later. The #ame position was always estimated by the tip of the visible #ame in the direction of spread. The rate of movement of the #ame tip will represent the speed of the pyrolysis front provided the speed is constant. For accelerating upward spread, the pyrolysis front speed would be less than #ame tip speed. All measurements were made under laboratory conditions of approximately 23$23C and 50$5% relative humidity.
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Table 1 Physical properties Material
Thickness () (mm)
Density () (g/cm)
Surface density () (g/m)
Met. PET Paper napkin Fiberglass
0.201 0.168 25.4
0.18 0.22 0.0095 or (0.59 lb/ft)
35.6 37.4 242.5
3. Theoretical model Several studies are signi"cant in constructing the theoretical model used. The important processes in #ame spread can be separated into two parts: (1) heat transfer to material ahead of the pyrolysis front, and (2) ignition of this newly heated material. The heat transfer can be taken from experimental or theoretical studies, and the ignition process is based on the concept of an ignition temperature for the solid. The latter assumes that chemical and di!usion gas phase e!ects are fast. The following concepts originate from a study on upward #ame spread over textiles at angles of 0}603 with the vertical [3]. Fig. 4 shows the typical #ame spread con"guration. The pyrolysis length is denoted by x and the #ame length is denoted by x as measured from the rear of the pyrolysis region. In Fig. 4, the #ame spread is shown, for convenience, to be simultaneously spreading up and down. In reality, there would be a burnout region following the `reara of the pyrolysis region in each case, which is not shown in Fig. 4. For a thermally thin material heated from one side by a #ame plume, #ame speed, or rate of change of x is given as q dx V " , (1) c(¹ !¹ ) where is density, is thickness, c is speci"c heat, T is ignition temperature, T is initial or ambient temperature and q is the net surface heat #ux to the material. Eq. (1) follows from an assumption of steady spread rate with a perfectly insulated back face. By considering an average heat #ux over the heat transfer length x !x , Eq. (1) can be written as x !x dx , v " " t dt where the ignition time is c(¹ !¹ ) . t " q
(2a)
(2b)
A similar result applies to thermally thick solids where the expression for t is changed to "t the thick condition. Again, this expression assumes that the pyrolysis
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Fig. 3. (a) Upward #ame spread, "03, napkin. (b). Downward #ame spread, "03, napkin. (c) Horizontal #ame spread, facing up, "#903, napkin. (d). Horizontal #ame spread, facing down, "!903, napkin. (e) Upward #ame spread, facing up, "#303, napkin. (f) Upward #ame spread, facing down, "!303, napkin. (g) Upward #ame spread, facing down, "!603, napkin.
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Fig. 4. Spread con"gurations and theoretical notation.
time to enable ignition is essentially the ignition time. Here, the denominator is the average heat #ux over the #ame extension. If we regard x as measured from the point of ignition (i.e., the pyrolysis point to enable ignition) and include the burnout position x (see Fig. 5), then dx , x (t#t )"x (t)+x (t)#t (3a) dt or x (t)!x (t) dx " , t dt where the burnout time is (1!) t " m
(3b)
(3c)
with m , the average mass loss #ux of the volatile fuel and , the char fraction. The complete problem of spread with burnout can be solved by computing the solution to the two ordinary di!erential equations (2a) and (3b). In order to do this, the following properties are needed: 1. material properties: , c, T , , 2. a burn rate relationship for m , and 3. a heat #ux relationship for q .
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Fig. 5. Upward spread with burnout.
As an alternative to solving the di!erential equations, an analysis was performed based on the measured #ame length for upward or gravity-assisted #ame spread. Figs. 6a and b give the observed #ame lengths for angles of 0, #30, #60, and #903 during spread for the napkin and PET, respectively. The increments shown are 1 in. and the #ame shape is drawn to scale. For these experiments, the napkin displayed a uniform #ame front as shown in Fig. 7a, indicative of one-dimensional surface spread. In contrast, the PET #ame spread was two-dimensional and was a!ected by curling in the direction of spread as shown in Fig. 7b. Since the theoretical results apply to a one-dimensional spread, only the napkin data will be analyzed. For the gravity-assisted analysis, the work of Faeth and coworkers [4}6] will be used. For the gravity-opposed case, the work of Kashiwagi et al. [7,8] will be used. These works will give the ability to compute the #ame heat #ux and heat transfer region (x !x ) needed to determine v from Eq. (2). Then a comparison can be made with measured #ame speeds.
3.1. Gravity-assisted yame spread Gravity-assisted spread is de"ned to occur when the component of gravity parallel to the surface is opposite to the spread direction, and consequently the corresponding buoyant force is assisting #ame spread. The thesis by Ahmad, under Faeth, will be the chief source of information in making calculations for the gravity-assisted burning rate and #ame length [5]. In these calculations, the pyrolysis and #ame length, x and x , will be measured from the start of pyrolysis region as shown in Fig. 4. (These results will be used in the context of Fig. 5 where x is x !x of Fig. 5). Ref. [5] contains both theoretical and experimental results for both laminar and turbulent #ows. The Grashof number, Gr , indicating the ratio of buoyant to viscous V forces is de"ned as
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Fig. 6. (a) Observed #ame lengths on napkins, increments 2.5 cm. (b) Observed #ame lengths on pet "lm, increments 2.5 cm.
g cos x Gr " , (4) V where g is the gravity force per unit mass, x is distance along the surface, and is the kinematic viscosity of the combustion products (approximated as air at T ). The onset of turbulence occurs at Gr "0.5;10 for "0 from which Eq. (4) gives V x"106 mm. Ahmad, however, achieved turbulent #ow for x"51 mm by tripping the boundary layer. The total length of material tested in Fig. 2 was 300 mm (12 in.). Hence, it is most likely that turbulent conditions prevailed. Nevertheless, laminar analysis will be included especially since it will be shown that laminar #ame spread can be much faster than the turbulent case. The burning rate analysis [4}6] has been based on steady conditions for an evaporating liquid fuel model. Liquid fuels (methanol, ethanol, and propanol) were saturated in an inert porous solid plate to obtain data. The dimensionless coe$cients presented herein will always be based on the `best-"ta experimental values for these fuels. The theoretical results will be used to estimate the behavior for other fuel properties. The equations hold as long as boundary layer #ows prevail, but as P903 for a plate facing upwards, detachment will occur. Theoretically the solution is said to hold up to $853 [5]. Dexnitions. The following parameters used in the analysis are de"ned here for clarity. Stoichiometric oxygen-to-fuel mass ratio, s. Available to stoichiometric oxygen}fuel ratio, r"(Y /Y )s\, where Y is the free stream oxygen mass fraction, Y is the $ 2 $ 2 transferred (solid or liquid) fuel mass fraction. Spalding B number: > (H /s) combustion energy ! " B" , ¸ evaporation energy
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Fig. 7. (a) Flame spread behavior on napkins. (b) Flame spread behavior on PET "lm.
c (¹ !¹ ) , " ¸ where c is the heat capacity of the gas, T is the wall vaporization temperature, L is the heat of gasi"cation (sensible plus phase change) and "r(B#1)/B(r#1) is $a #ame locus parameter. Prandtl number, Pr"/ , is the ratio of viscous di!usion to thermal di!usion (taken as 0.73) modi"ed Grashof number, GH"(¸/4c ¹ )Gr . P V Laminar. The burning rate per unit area, m , can be determined from m x Pr GrH V "C (B, Pr, , ), (5) K * $- B where is the viscosity of the gas (20;10\ N s\) and C is primarily a function K * of B. Table 2 shows the selected coe$cients for the fuels [4}6] with their properties where C , C , and C are the empirical coe$cient for laminar burning rate, D * O * O 2
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Table 2 Liquid fuel properties Fuel
s
r (air)
L (kJ/g)
Methanol Ethanol Propanol
1.51 2.10 2.68
0.154 0.111 0.087
1.23 0.880 0.788
0.044 0.087 0.134
T (K)
H (kJ/g)
B
C K *
C D *
C O *
C O 2
337 352 370
19.1 25.6 29.0
2.60 3.41 3.71
0.29 0.27 0.25
4.8 9.0 11.0
0.53 0.55 0.59
0.030 0.038 0.040
Fig. 8. Empirical coe$cients as a function of B.
laminar heat #ux, and turbulent heat #ux, respectively. Fig. 8 shows an empirical "t as a function of B. The average burning rate over length x can be determined from Eq. (5) as
1 V 4 m (x)" m dx" m (x). x 3 The #ame length measured from the start of the pyrolysis region is found as
(6)
x "C , (7) D * x where C (Table 1) depends on the fuel. D * Roper et al. [9] "nd for a buoyancy-controlled slot burner in air at volumetric fuel #ow rate per unit length,
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where T and T are fuel and #ame temperatures, respectively, and is a function of S, $ the molar stoichiometric oxidizer to fuel ratio. for a slot burner: 1
" . 4 inv [erf (1/1#S)]
(9a)
and for a circular burner: 1
" +S for large S. ln (1#1/S)
(9b)
Rearrangement of Eqs. (7) and (8) show their similarity and allows for some generalizations. From Eqs. (5) and (6) with the energy release rate per unit lateral dimension of the wall QQ "H m x it can be shown that Eq. (7) can be written as
c ¹ l 3 Pr c ¹ . C D * C B H 4 ¸ l K * The characteristic length scales are the plume convective length x"
QQ l " c ¹ (g cos and plume viscous length
(10)
(11)
(12)
l " . (g cos
(13)
By recognizing H V H "H /s+13.6 kJ/g. V Eq. (11) can be approximated as B¸+>
C (3Pr) c ¹ l D * s . x+ (14) 4> H BC s l V K * It is found that C /BC s+7.0$0.5 for the three experimental liquid fuels. *
* Substituting ¹ "298 K, c "10\ kJ/g, and Pr"0.73, the Ahmad-Faeth equation can be expressed as s x "0.023 >
l . l
(15)
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The result by Roper et al., Eq. (8), can also be put into this form (dropping the T -term) l ¹ c ¹ , x "C s 0 ¹ H l $ V where C is a constant. 0 If the approximation in Eq. (9b) is used, Roper's equation becomes
l ¹ c ¹ S (16) l ¹ H $ V which is very similar to Eq. (14). The heat #ux in the pyrolysis region is approximately constant and determined by x +C 0
q "m (x )¸. (17) * In the `over-"rea region or where the #ame extends (x !x ), the heat #ux can be approximated as constant by q x Pr Gr\ * V "C (18) O * B, ¸ S where C is given in Table 1 and Fig. 8. A typical result from Ahmad [5] is shown in O * Fig. 9 and illustrates the complete distribution within and beyond the #ame. Turbulent. The corresponding turbulent results derived from Ref. [5] follow. Burning rate: m xPr GrH\ 0.0285 V " , where
(19a)
1#0.5Pr/(1#B) 1#B , (19b) B ln(1#B) 3(B# ) # (19c) "1! $with +0.43 for methanol and +0.33 for cellulose and PET. Recall, from the de"nitions, "
r(B#1)
" . $B(r#1) Flame height: 1.02l , (20) (1!X ) where X is the #ame radiative fraction. Values for the #ame radiative fraction for the liquid fuels were calculated from the total energy release rate and the radiative heat x " 2 >
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303
Fig. 9. Wall heat #ux.
#ux lost to the wall and the surroundings as tabulated in Table 7 of Ref. [5]. These were found to range from 0.06 to 0.12 with an average of about 0.10 for all of the liquids. Fig. 10 shows this result for #ame height plotted against data taken from Ref. [5]. The #ame length was inferred from distributions of the wall heat #ux at the position where the measured heat #ux signi"cantly dropped in the over-"re region. Eq. (20) is consistent with well-known results for wall #ames in air (e.g., Fernandez-Pello [10] where the coe$cient of l ranges from 4.5 to 8.0). The dependencies in Y and X come from results for line "res by Quintiere and Grove [11]. Using values Y "0.233 and X "0.1, the coe$cient is computed as 4.5 in Eq. (20). Since the interpretation of the Faeth et al. [4}6], #ame length data are based on the position of a sharp decrease in the heat #ux; this coe$cient of 4.5 likely corresponds to a length within the #ickering #ame zone. Flame heat #ux: The heat #ux in the over-"re region is based on the total incident heat #ux. An empirical result for the average #ame heat #ux is given by q x Pr GrH\ 2 V "C * B¸
(21)
with the empirical correlation for the coe$cient given in Fig. 8. Results from Ahmad [5] are shown in Fig. 11 for ethanol. They show the complete heat #ux distribution
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Fig. 10. Wall #ame height correlation based on data from Ahmad [5].
into the wall plume beyond the #ame. Both the turbulent and laminar correlations for #ame heat #ux assume constant heat #ux over the #ame region and ignore the contribution by the wall plume.
3.2. Gravity opposed yame spread For opposed #ow #ame spread, the #ame heat transfer is needed at the `nosea of the #ame as depicted in Fig. 4. In the theoretical solution by DeRis [12] for thermally thin (i.e., )1 to 2 mm) materials, the opposed #ow #ame speed is (2k (¹ !¹ ) , v " ()c(¹ !¹ )
(22)
where k is the thermal conductivity of the gas. No dependence on gravity-induced #ow velocity occurs. The #ame temperature can be regarded as nearly constant provided there are gas-phase retardants or diluents that can decompose from the material. The polymethyl-methacrylate (PMMA) data of Ito and Kashiwagi [8] should have this character enabling their data on heat #ux and the #ame heating region to be somewhat generic, or an upper limit in the least for heat #ux. Their results for the forward heat #ux distributions are shown in Fig. 12 as a function of angle , the complement of ("!90! ). The heat #ux measured is the absorbed or net surface heat #ux. An average heat #ux was determined by the area
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Fig. 11. Wall heat #ux for ethanol taken from Ahmad [5] (x is pyrolysis length).
under the curves for q *20 kW/m and the heat transfer region (x !x ) de"ned by length corresponding to 20 kW/m. These results are plotted in Fig. 13 for downward as well as upward spread for the range of their data. Since the vaporization temperature reported for this PMMA was 3803C, corresponding to a re-radiation #ux of 10 kW/m, the incident #ux could be up to 10 kW/m higher. The lower limit values as shown in Fig. 13 will be used in the analysis to follow.
4. Results The computations for #ame spread will be made using the equations and data presented in the previous section. Properties will be assembled, as best estimates, for the brown paper towel (napkin) and the insulation "lm (MPET). 4.1. Experimental The experimental results are shown in Figs. 14 and 15 for the napkin and MPET. The frequency of extinguishment of the #ame front during propagation over the
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Fig. 12. Heat #ux ahead of the #ame from Ito and Kashiwagi [8].
Fig. 13. Average #ame heat #ux and heated length in opposed #ow #ame spread derived from Ito and Kashiwagi [8].
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Fig. 14. Frequency of extinguishment during #ame spread.
Fig. 15. Flame spread velocity.
30.5-cm sample lengths (Fig. 14) shows the wide variation of the MPET in its ability to maintain sustained #ame spread. It appears that the highest frequency of extinguishment occurred for spread on the top or upward facing surface of the MPET. In contrast, the napkin was nearly free of extinguishment. Despite the frequent extinguishment of the MPET, the measured #ame speeds for the MPET and napkin are very similar. Downward spread on the top surface is nearly constant from 0 to #903 at about 1}2 mm/s. Downward spread on the bottom surface distinctly increases at about !603. This transition is consistent with results by Kashiwagi and Newman [7] for 1-mm -cellulose sheets, and by Hirano et al. [18] for 0.16 mm computer cards. The upward burning on the top surface shows an increase in speed as the sample becomes more vertical with a transition between at about 603 or above. Drysdale and Macmillian [19] report this transition at 80}853 for thick samples of PMMA. Kashiwagi and Newman [7] reported that the #ame on the
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Table 3 Thin-material properties Material
(kg/m)
c (kJ/kg-K)
L (kJ/kg)
H (kJ/g)
T (3C)
B
X
Napkin MPET
0.0374 0.0320
1.34 1.0
3000 3000
11,400 21,300
350 450
0.91 0.86
0.1 0.1
Incropera and DeWitt [13]. Babrauskas [14]. Lyon [15]. Tewarson [16]. Kashiwagi and Newman [17]. Van Krevelin [7].
top surface separates from the surface at "603 and remained more boundary layer-like below 603. Figs. 6a and b reveal this as well. The upward spread in the bottom surface is most severe since it maintains its boundary layer character for all angles up to !903 and results in long #ame lengths. Although most of the data remained steady, upward spread near the vertical was accelerating with speeds of 30}60 mm/s. 4.2. Theoretical The #ame speeds were computed as a function of angle, orientation, and direction. While they could be computed from Eqs. (2) and (3) together with the #ame length and heat #ux correlations, it was decided to use measured #ame lengths (for upward spread) to compute v directly from Eq. (2). For turbulent upward spread, the procedure was to compute m x from Eq. (20), x from Eq. (19), and q from Eq. (18). The corresponding laminar speeds, for the measured #ame length, will not be reported. They were signi"cantly higher than the turbulent speeds. Downward and nearly horizontal spread on the top surface was computed from the heat #ux and #ame-heated length as given in Fig. 13. The ignition time was computed from Eq. (2b). Properties needed in the computations were estimated from literature values and are given in Table 3. The e!ect of temperatures on speci"c heat was estimated by c"1.5c . Fig. 16 gives the #ame length as measured parallel to the surface and in the direction of spread from the start of pyrolysis. These lengths were estimated from video frames and are not unique when upward acceleration occurred. These values were used to compute the gravity-assisted #ame speeds. The #ame lengths given in Fig. 16 are the total #ame length including the pyrolysis region and should not be confused with the #ame extension or heat transfer length, x !x . Gas phase properties were taken as: "1.2 kg/m, c "1.0 kJ/kg K (air stream), T "298 K,
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Fig. 16. Flame length measured parallel to the surface.
"15.3;10\ m/s, Pr"0.73, c "1.4 kJ/kg K (fuel stream). It can be shown that in units of kg, kJ, m, and s the equations needed to predict gravity-assisted #ame spread can be expressed as follows: (m x )"116(cos ) x /H , 2 x "454.3((m x )) /(¸ cos ) , m "(m x )/x , q "m ¸, and q "C B¸(cos ¸) x . * Then we have su$cient information to compute the speed from Eq. (2), v " (x !x )/t . For gravity opposed spread, Eq. (2) can be directly implemented from the #ame heat transfer information given in Fig. 13. The computed results are shown in Fig. 17 and labeled according to the correlations of Ahmad and Faeth (AF) and Ito and Kashiwagi (IK). The predictive results appear to follow the data with reasonable agreement.
5. Discussion Previous studies on the e!ect of inclination on #ame spread have addressed thin materials burning on two sides [3,7,18,19] and thick materials burning on one side
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Fig. 17. Comparison of predicted and measured #ame speeds for the napkin.
[8,19]. All show consistency with the current study of a thin material burning on one side only. They show a critical angle for transition to increasing spread rate for downward spread on the bottom at "!603, and for upward spread on the top at "#603 where the #ame attaches to the surfaces in the boundary layer. From Fig. 17, it is obvious from both theory and experiment that the most serious #ame spread hazard, in terms of speed, is vertical upward spread. Flame spread downward, on either top or bottom, is less than 4 mm/s for all angles except for the bottom horizontal orientation at which it nearly doubles to 9 mm/s. Upward spread on the bottom is generally faster than upward spread on the top. The #ame heat #ux is higher (&50 kW/m) for downward or gravity opposed spread than for upward or gravity-assisted spread with heat #uxes of &10}20 kW/m for angles of 03 to $603. The relatively large #ame heated length for upward spread, roughly 4 cm, causes the higher spread rate for this orientation. Between !753 and 303, GrH was at least 10 VN implying turbulent #ow for all of the gravity-assisted cases. Computed results for the MPET "lm gave similar results to the napkin material. However, the one-dimensional #ame spread theory would not apply to the twodimensional burning as illustrated in Fig. 7b. Although laminar burning conditions did not appear relevant, computations showed that the gravity-assisted cases yielded heat #uxes as high as 50 kW/m and speeds up to 500 mm/s. This suggests that in small #ame tests, such as Bunsen burner ignition tests, the initial #ame speed could be high due to laminar conditions. This will occur before the onset of turbulent #ow. Such results can be misleading and erratic since many sources of disturbance can in#uence the transition to turbulent #ames. Finally, it should be emphasized that the #ame spread speeds reported here apply to comparable conditions of scale and ambient environment. Where accelerating #ames
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might occur for larger scale upward conditions, higher velocities will prevail. Where thermal environments in a developing compartment "re might occur, thermally enhanced speeds will occur.
6. Conclusions This study has shown the e!ect of orientation on #ame spread over thin "lms. It has shown that satisfactory predictive results could be achieved based on general correlations and data in the literature. In the process of executing this analysis, relationships for #ame length were developed for both laminar and turbulent burning of walls. These are consistent with other results in the literature. With respect to safety issues, upward #ame spread is the most serious "re hazard, and upward spread on the bottom of the inclined surface is more hazardous than that corresponding to the top.
Acknowledgements The author is indebted to Sanjeev Gandhi and Sean Crowley for their help in designing the test apparatus and conducting the experiments, to Richard Lyon for his helpful discussions, and to Patricia Cahill for useful discussions and guidance on the #ammability and characteristics of thin "lm acoustic insulation.
References [1] Cahill P. Evaluation of "re test methods for aircraft thermal acoustical insulation. DOT/FAA/AR97/58, September 1997. [2] Cahill P. Private communication, FAA, Atlantic City International Airport, NJ, 1999. [3] Markstein GH, DeRis J. Upward "re spread over textiles. Proceedings of the 14th International Symposium on Combustion, The Combustion Institute, 1973. p. 1085. [4] Ahmad T, Gro! EG, Faeth GM. Fire-induced plumes along a vertical wall: Part II: the Laminar combusting region, Mechanical Engineering Department, The Pennsylvania State University, July 1977. [5] Ahmad T. Investigation of the combusting region of "re-induced plumes along upright surfaces. Ph.D. thesis, The Pennsylvania State University, August 1978. [6] Ahmad T, Faeth GM. Turbulent wall "res, Proceedings of the 17th Symposium on Combustion, The Combustion Institute, 1978. p. 1149. [7] Kashiwagi T, Newman DL. Flame spread over an inclined thin fuel surface. Combust Flame 1976;26:163. [8] Ito A, Kashiwagi T. Characterization of #ame spread over PMMA using holographic interferometry sample orientation e!ects. Combust Flame 1988;71:189. [9] Roper FG, Smith C, Cunningham AC. The prediction of Laminar jet di!usion #ame sizes: Part II: experimental veri"cation. Combust Flame 1977;29:227. [10] Fernandez Pello AC. The solid phase. In: Cox G, editor. Fundamentals of Fire and Combustion. London: Academic Press, 1995. [11] Quintiere JG, Grove BS. A uni"ed analysis for "re plumes. Proceedings of the 27th Symposium on Combustion, The Combustion Institute, 1998. p. 2757.
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[12] DeRis J. The spread of laminar di!usion #ame. Proceedings of the 12th International Symposium on Combustion, The Combustion Institute, 1969. p. 241. [13] Incropera FP, DeWitt DP. Fundamentals of heat and mass transfer, 3rd ed. New York: Wiley, 1990. p. A14. [14] Babrauskas V. Related quantities. In: Babrauskas V, Greyson SJ, editors. Heat release in "res. London: Elsevier Applied Science, 1992. p. 214. [15] Lyon RE. Solid-state thermochemistry of #aming combustion. DOT/FAA/AR-99/56, July 1999. [16] Tewarson A. Generation of heat and chemical compounds in "res. In: SFPE handbook of "re protection engineering, 2nd ed. Quincy, MA: NFPA, 1995. p. 3}78. [17] Van Krevelin DW. Properties of polymers. Amsterdam: Elsevier, 1990. p. 642. [18] Hirano T, Noreikis SE, Waterman TE. Postulations of #ame spread mechanisms. Combust Flame 1974;22:353}63. [19] Drysdale DD, Macmillan ARJ. Flame spread on inclined surfaces. Fire Safety J 1992;18:245}54.
The e!ects of angular orientation on #ame spread over thin materials James G. Quintiere* Department of Fire Protection Engineering, University of Maryland, Building 88, College Park, MD 20742, USA Received 5 April 2000; received in revised form 16 August 2000; accepted 13 September 2000
Abstract Data were taken to show the #ame spread characteristics of thin materials burning on an insulating substrate. Metalized polyethylene terephthalate (0.20 mm) and paper (0.17 mm) were burned on the surface of glass "ber insulation. Flame spread was measured in the upward or downward facing orientation for the material and in the directions of gravity assistance (up) or gravity opposition (down). Measurements were taken at various angles ranging from a vertical to a horizontal orientation. A theoretical analysis was developed to predict the #ame spread as a function of material properties, sample orientation, and #ame spread direction. The onedimensional theory was in reasonable agreement with the paper data. Vertical upward spread was found to yield the highest velocity. Critical angles (measured from the vertical) show transition to increasing #ame spread for downward bottom spread at !603, and for upward top surface spread at 603. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Flame spread; Thin materials; Direction; Inclination; Angle
1. Introduction This study was motivated by the need to investigate the #ammability of aircraft thermal}acoustical insulation blankets. In particular, it considers the thin "lm which encapsulates the insulation material. Blankets of this insulation lines the interior skin of aircraft cabins to reduce the noise and heat transfer. Two small-scale #ame spread tests apply to thermal}acoustical insulation blankets. The "rst is a regulatory requirement contained in FAR 25.853, a vertical Bunsen burner test. The second is an industry standard called the `cotton swab testa, which * Corresponding author. Tel.: #1-301-405-3993; fax: #1-301-405-9383. E-mail address: [email protected] (J.G. Quintiere). 0379-7112/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 0 ) 0 0 0 5 1 - 5
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Fig. 1. Flame spread on a metalized pet-"berglass insulation "lm after ignition by an electrical arc.
consists of ignition by alcohol-soaked cotton swabs inserted in the center of a horizontal sample and at the crease it makes with a vertical section [1]. Attempts to simulate realistic ignition sources were conducted by Cahill [2]. One example, of upward and downward spread on a metalized polyethylene terephthalate (PET) "lm insulation blanket is shown in Fig. 1 on a curved aircraft cabin section. The maximum upward burnout region (U ), downward pyrolysis region (D ), and upward #ame length (L ) were measured from a video recording of the test. Despite erratic burn fronts with discontinuous #aming regions, the maximum speeds and #ame lengths appear approximately constant at speeds of 5.9 mm/s up, 2.6 mm/s down, and lengths of 120 mm for the upward #ames. It was generally found that the ignition and sustained #ame spread of typical aircraft insulation blanket "lms were di$cult to achieve by small #ame sources. Some speculated that Bunsen burner type testing for samples oriented downward and 453 with the vertical gave more consistent spread. As a consequence, it was decided to investigate the e!ect of orientation and inclination angle on the #ame spread of thin "lms. A metalized PET "lm, which seemed easily ignitable by a small #ame, was selected as a representative aircraft material. Later it was found that a thin-paper specimen gave more consistent one-dimensional #ame spread results. Both upward and downward #ame spread were examined.
2. Experimental arrangement The experimental test apparatus consisted of a steel holder that could sandwich a test sample "lm against "berglass insulation without compression. The apparatus is shown in Fig. 2. A grid was inscribed at 0.5-in. (1.27-cm) increments on each outward facing steel longitudinal edge. This enabled an observer to identify the #ame position.
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293
Fig. 2. Flame spread apparatus.
A digital clock was positioned so that the time and #ame position could be simultaneously viewed on a video recording. For burning on the underside of the sample, a mirror was positioned to observe the clock and the #ame progression. A rod attached to one face of the steel holder and a clamp arrangement allowed the assembly to be rotated. A level gage and protractor was used to set the angle, , to the vertical. A small butane di!usion #ame approximately 1}2 cm in length and 1 cm in diameter was used to ignite the "lm sample. Once ignition occurred, the igniter was withdrawn. If #ame spread terminated before the end of the 12-in. (30.5-cm) sample length, the igniter was reapplied. This was repeated as necessary. Two samples were tested. The "rst was representative of aircraft thermal}acoustical "lms; the second was a brown paper towel (napkin) commonly found in dispensers for drying hands. The latter was selected because the metalized polyethylene terephthalate (PET) did not always sustain #ame spread, and a more consistent material was desired. It was found that the paper napkin did yield similar results to the PET, and it also had similar properties. Component material properties are shown in Table 1. The samples were tested over angles ranging from 903 (vertical) to 03 (horizontal). A designation of `#a represents an upward facing sample (top) and `!a a downward facing sample (bottom). Both upward and downward spread were examined. Figs. 3a}g display the progression of the #ame tip position as a function of time for the paper napkin. Note that the time-scale zero point was arbitrarily selected, and ignition was started later. The #ame position was always estimated by the tip of the visible #ame in the direction of spread. The rate of movement of the #ame tip will represent the speed of the pyrolysis front provided the speed is constant. For accelerating upward spread, the pyrolysis front speed would be less than #ame tip speed. All measurements were made under laboratory conditions of approximately 23$23C and 50$5% relative humidity.
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Table 1 Physical properties Material
Thickness () (mm)
Density () (g/cm)
Surface density () (g/m)
Met. PET Paper napkin Fiberglass
0.201 0.168 25.4
0.18 0.22 0.0095 or (0.59 lb/ft)
35.6 37.4 242.5
3. Theoretical model Several studies are signi"cant in constructing the theoretical model used. The important processes in #ame spread can be separated into two parts: (1) heat transfer to material ahead of the pyrolysis front, and (2) ignition of this newly heated material. The heat transfer can be taken from experimental or theoretical studies, and the ignition process is based on the concept of an ignition temperature for the solid. The latter assumes that chemical and di!usion gas phase e!ects are fast. The following concepts originate from a study on upward #ame spread over textiles at angles of 0}603 with the vertical [3]. Fig. 4 shows the typical #ame spread con"guration. The pyrolysis length is denoted by x and the #ame length is denoted by x as measured from the rear of the pyrolysis region. In Fig. 4, the #ame spread is shown, for convenience, to be simultaneously spreading up and down. In reality, there would be a burnout region following the `reara of the pyrolysis region in each case, which is not shown in Fig. 4. For a thermally thin material heated from one side by a #ame plume, #ame speed, or rate of change of x is given as q dx V " , (1) c(¹ !¹ ) where is density, is thickness, c is speci"c heat, T is ignition temperature, T is initial or ambient temperature and q is the net surface heat #ux to the material. Eq. (1) follows from an assumption of steady spread rate with a perfectly insulated back face. By considering an average heat #ux over the heat transfer length x !x , Eq. (1) can be written as x !x dx , v " " t dt where the ignition time is c(¹ !¹ ) . t " q
(2a)
(2b)
A similar result applies to thermally thick solids where the expression for t is changed to "t the thick condition. Again, this expression assumes that the pyrolysis
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Fig. 3. (a) Upward #ame spread, "03, napkin. (b). Downward #ame spread, "03, napkin. (c) Horizontal #ame spread, facing up, "#903, napkin. (d). Horizontal #ame spread, facing down, "!903, napkin. (e) Upward #ame spread, facing up, "#303, napkin. (f) Upward #ame spread, facing down, "!303, napkin. (g) Upward #ame spread, facing down, "!603, napkin.
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Fig. 4. Spread con"gurations and theoretical notation.
time to enable ignition is essentially the ignition time. Here, the denominator is the average heat #ux over the #ame extension. If we regard x as measured from the point of ignition (i.e., the pyrolysis point to enable ignition) and include the burnout position x (see Fig. 5), then dx , x (t#t )"x (t)+x (t)#t (3a) dt or x (t)!x (t) dx " , t dt where the burnout time is (1!) t " m
(3b)
(3c)
with m , the average mass loss #ux of the volatile fuel and , the char fraction. The complete problem of spread with burnout can be solved by computing the solution to the two ordinary di!erential equations (2a) and (3b). In order to do this, the following properties are needed: 1. material properties: , c, T , , 2. a burn rate relationship for m , and 3. a heat #ux relationship for q .
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297
Fig. 5. Upward spread with burnout.
As an alternative to solving the di!erential equations, an analysis was performed based on the measured #ame length for upward or gravity-assisted #ame spread. Figs. 6a and b give the observed #ame lengths for angles of 0, #30, #60, and #903 during spread for the napkin and PET, respectively. The increments shown are 1 in. and the #ame shape is drawn to scale. For these experiments, the napkin displayed a uniform #ame front as shown in Fig. 7a, indicative of one-dimensional surface spread. In contrast, the PET #ame spread was two-dimensional and was a!ected by curling in the direction of spread as shown in Fig. 7b. Since the theoretical results apply to a one-dimensional spread, only the napkin data will be analyzed. For the gravity-assisted analysis, the work of Faeth and coworkers [4}6] will be used. For the gravity-opposed case, the work of Kashiwagi et al. [7,8] will be used. These works will give the ability to compute the #ame heat #ux and heat transfer region (x !x ) needed to determine v from Eq. (2). Then a comparison can be made with measured #ame speeds.
3.1. Gravity-assisted yame spread Gravity-assisted spread is de"ned to occur when the component of gravity parallel to the surface is opposite to the spread direction, and consequently the corresponding buoyant force is assisting #ame spread. The thesis by Ahmad, under Faeth, will be the chief source of information in making calculations for the gravity-assisted burning rate and #ame length [5]. In these calculations, the pyrolysis and #ame length, x and x , will be measured from the start of pyrolysis region as shown in Fig. 4. (These results will be used in the context of Fig. 5 where x is x !x of Fig. 5). Ref. [5] contains both theoretical and experimental results for both laminar and turbulent #ows. The Grashof number, Gr , indicating the ratio of buoyant to viscous V forces is de"ned as
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Fig. 6. (a) Observed #ame lengths on napkins, increments 2.5 cm. (b) Observed #ame lengths on pet "lm, increments 2.5 cm.
g cos x Gr " , (4) V where g is the gravity force per unit mass, x is distance along the surface, and is the kinematic viscosity of the combustion products (approximated as air at T ). The onset of turbulence occurs at Gr "0.5;10 for "0 from which Eq. (4) gives V x"106 mm. Ahmad, however, achieved turbulent #ow for x"51 mm by tripping the boundary layer. The total length of material tested in Fig. 2 was 300 mm (12 in.). Hence, it is most likely that turbulent conditions prevailed. Nevertheless, laminar analysis will be included especially since it will be shown that laminar #ame spread can be much faster than the turbulent case. The burning rate analysis [4}6] has been based on steady conditions for an evaporating liquid fuel model. Liquid fuels (methanol, ethanol, and propanol) were saturated in an inert porous solid plate to obtain data. The dimensionless coe$cients presented herein will always be based on the `best-"ta experimental values for these fuels. The theoretical results will be used to estimate the behavior for other fuel properties. The equations hold as long as boundary layer #ows prevail, but as P903 for a plate facing upwards, detachment will occur. Theoretically the solution is said to hold up to $853 [5]. Dexnitions. The following parameters used in the analysis are de"ned here for clarity. Stoichiometric oxygen-to-fuel mass ratio, s. Available to stoichiometric oxygen}fuel ratio, r"(Y /Y )s\, where Y is the free stream oxygen mass fraction, Y is the $ 2 $ 2 transferred (solid or liquid) fuel mass fraction. Spalding B number: > (H /s) combustion energy ! " B" , ¸ evaporation energy
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299
Fig. 7. (a) Flame spread behavior on napkins. (b) Flame spread behavior on PET "lm.
c (¹ !¹ ) , " ¸ where c is the heat capacity of the gas, T is the wall vaporization temperature, L is the heat of gasi"cation (sensible plus phase change) and "r(B#1)/B(r#1) is $a #ame locus parameter. Prandtl number, Pr"/ , is the ratio of viscous di!usion to thermal di!usion (taken as 0.73) modi"ed Grashof number, GH"(¸/4c ¹ )Gr . P V Laminar. The burning rate per unit area, m , can be determined from m x Pr GrH V "C (B, Pr, , ), (5) K * $- B where is the viscosity of the gas (20;10\ N s\) and C is primarily a function K * of B. Table 2 shows the selected coe$cients for the fuels [4}6] with their properties where C , C , and C are the empirical coe$cient for laminar burning rate, D * O * O 2
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Table 2 Liquid fuel properties Fuel
s
r (air)
L (kJ/g)
Methanol Ethanol Propanol
1.51 2.10 2.68
0.154 0.111 0.087
1.23 0.880 0.788
0.044 0.087 0.134
T (K)
H (kJ/g)
B
C K *
C D *
C O *
C O 2
337 352 370
19.1 25.6 29.0
2.60 3.41 3.71
0.29 0.27 0.25
4.8 9.0 11.0
0.53 0.55 0.59
0.030 0.038 0.040
Fig. 8. Empirical coe$cients as a function of B.
laminar heat #ux, and turbulent heat #ux, respectively. Fig. 8 shows an empirical "t as a function of B. The average burning rate over length x can be determined from Eq. (5) as
1 V 4 m (x)" m dx" m (x). x 3 The #ame length measured from the start of the pyrolysis region is found as
(6)
x "C , (7) D * x where C (Table 1) depends on the fuel. D * Roper et al. [9] "nd for a buoyancy-controlled slot burner in air at volumetric fuel #ow rate per unit length,
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301
where T and T are fuel and #ame temperatures, respectively, and is a function of S, $ the molar stoichiometric oxidizer to fuel ratio. for a slot burner: 1
" . 4 inv [erf (1/1#S)]
(9a)
and for a circular burner: 1
" +S for large S. ln (1#1/S)
(9b)
Rearrangement of Eqs. (7) and (8) show their similarity and allows for some generalizations. From Eqs. (5) and (6) with the energy release rate per unit lateral dimension of the wall QQ "H m x it can be shown that Eq. (7) can be written as
c ¹ l 3 Pr c ¹ . C D * C B H 4 ¸ l K * The characteristic length scales are the plume convective length x"
QQ l " c ¹ (g cos and plume viscous length
(10)
(11)
(12)
l " . (g cos
(13)
By recognizing H V H "H /s+13.6 kJ/g. V Eq. (11) can be approximated as B¸+>
C (3Pr) c ¹ l D * s . x+ (14) 4> H BC s l V K * It is found that C /BC s+7.0$0.5 for the three experimental liquid fuels. *
* Substituting ¹ "298 K, c "10\ kJ/g, and Pr"0.73, the Ahmad-Faeth equation can be expressed as s x "0.023 >
l . l
(15)
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The result by Roper et al., Eq. (8), can also be put into this form (dropping the T -term) l ¹ c ¹ , x "C s 0 ¹ H l $ V where C is a constant. 0 If the approximation in Eq. (9b) is used, Roper's equation becomes
l ¹ c ¹ S (16) l ¹ H $ V which is very similar to Eq. (14). The heat #ux in the pyrolysis region is approximately constant and determined by x +C 0
q "m (x )¸. (17) * In the `over-"rea region or where the #ame extends (x !x ), the heat #ux can be approximated as constant by q x Pr Gr\ * V "C (18) O * B, ¸ S where C is given in Table 1 and Fig. 8. A typical result from Ahmad [5] is shown in O * Fig. 9 and illustrates the complete distribution within and beyond the #ame. Turbulent. The corresponding turbulent results derived from Ref. [5] follow. Burning rate: m xPr GrH\ 0.0285 V " , where
(19a)
1#0.5Pr/(1#B) 1#B , (19b) B ln(1#B) 3(B# ) # (19c) "1! $with +0.43 for methanol and +0.33 for cellulose and PET. Recall, from the de"nitions, "
r(B#1)
" . $B(r#1) Flame height: 1.02l , (20) (1!X ) where X is the #ame radiative fraction. Values for the #ame radiative fraction for the liquid fuels were calculated from the total energy release rate and the radiative heat x " 2 >
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303
Fig. 9. Wall heat #ux.
#ux lost to the wall and the surroundings as tabulated in Table 7 of Ref. [5]. These were found to range from 0.06 to 0.12 with an average of about 0.10 for all of the liquids. Fig. 10 shows this result for #ame height plotted against data taken from Ref. [5]. The #ame length was inferred from distributions of the wall heat #ux at the position where the measured heat #ux signi"cantly dropped in the over-"re region. Eq. (20) is consistent with well-known results for wall #ames in air (e.g., Fernandez-Pello [10] where the coe$cient of l ranges from 4.5 to 8.0). The dependencies in Y and X come from results for line "res by Quintiere and Grove [11]. Using values Y "0.233 and X "0.1, the coe$cient is computed as 4.5 in Eq. (20). Since the interpretation of the Faeth et al. [4}6], #ame length data are based on the position of a sharp decrease in the heat #ux; this coe$cient of 4.5 likely corresponds to a length within the #ickering #ame zone. Flame heat #ux: The heat #ux in the over-"re region is based on the total incident heat #ux. An empirical result for the average #ame heat #ux is given by q x Pr GrH\ 2 V "C * B¸
(21)
with the empirical correlation for the coe$cient given in Fig. 8. Results from Ahmad [5] are shown in Fig. 11 for ethanol. They show the complete heat #ux distribution
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Fig. 10. Wall #ame height correlation based on data from Ahmad [5].
into the wall plume beyond the #ame. Both the turbulent and laminar correlations for #ame heat #ux assume constant heat #ux over the #ame region and ignore the contribution by the wall plume.
3.2. Gravity opposed yame spread For opposed #ow #ame spread, the #ame heat transfer is needed at the `nosea of the #ame as depicted in Fig. 4. In the theoretical solution by DeRis [12] for thermally thin (i.e., )1 to 2 mm) materials, the opposed #ow #ame speed is (2k (¹ !¹ ) , v " ()c(¹ !¹ )
(22)
where k is the thermal conductivity of the gas. No dependence on gravity-induced #ow velocity occurs. The #ame temperature can be regarded as nearly constant provided there are gas-phase retardants or diluents that can decompose from the material. The polymethyl-methacrylate (PMMA) data of Ito and Kashiwagi [8] should have this character enabling their data on heat #ux and the #ame heating region to be somewhat generic, or an upper limit in the least for heat #ux. Their results for the forward heat #ux distributions are shown in Fig. 12 as a function of angle , the complement of ("!90! ). The heat #ux measured is the absorbed or net surface heat #ux. An average heat #ux was determined by the area
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305
Fig. 11. Wall heat #ux for ethanol taken from Ahmad [5] (x is pyrolysis length).
under the curves for q *20 kW/m and the heat transfer region (x !x ) de"ned by length corresponding to 20 kW/m. These results are plotted in Fig. 13 for downward as well as upward spread for the range of their data. Since the vaporization temperature reported for this PMMA was 3803C, corresponding to a re-radiation #ux of 10 kW/m, the incident #ux could be up to 10 kW/m higher. The lower limit values as shown in Fig. 13 will be used in the analysis to follow.
4. Results The computations for #ame spread will be made using the equations and data presented in the previous section. Properties will be assembled, as best estimates, for the brown paper towel (napkin) and the insulation "lm (MPET). 4.1. Experimental The experimental results are shown in Figs. 14 and 15 for the napkin and MPET. The frequency of extinguishment of the #ame front during propagation over the
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Fig. 12. Heat #ux ahead of the #ame from Ito and Kashiwagi [8].
Fig. 13. Average #ame heat #ux and heated length in opposed #ow #ame spread derived from Ito and Kashiwagi [8].
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Fig. 14. Frequency of extinguishment during #ame spread.
Fig. 15. Flame spread velocity.
30.5-cm sample lengths (Fig. 14) shows the wide variation of the MPET in its ability to maintain sustained #ame spread. It appears that the highest frequency of extinguishment occurred for spread on the top or upward facing surface of the MPET. In contrast, the napkin was nearly free of extinguishment. Despite the frequent extinguishment of the MPET, the measured #ame speeds for the MPET and napkin are very similar. Downward spread on the top surface is nearly constant from 0 to #903 at about 1}2 mm/s. Downward spread on the bottom surface distinctly increases at about !603. This transition is consistent with results by Kashiwagi and Newman [7] for 1-mm -cellulose sheets, and by Hirano et al. [18] for 0.16 mm computer cards. The upward burning on the top surface shows an increase in speed as the sample becomes more vertical with a transition between at about 603 or above. Drysdale and Macmillian [19] report this transition at 80}853 for thick samples of PMMA. Kashiwagi and Newman [7] reported that the #ame on the
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Table 3 Thin-material properties Material
(kg/m)
c (kJ/kg-K)
L (kJ/kg)
H (kJ/g)
T (3C)
B
X
Napkin MPET
0.0374 0.0320
1.34 1.0
3000 3000
11,400 21,300
350 450
0.91 0.86
0.1 0.1
Incropera and DeWitt [13]. Babrauskas [14]. Lyon [15]. Tewarson [16]. Kashiwagi and Newman [17]. Van Krevelin [7].
top surface separates from the surface at "603 and remained more boundary layer-like below 603. Figs. 6a and b reveal this as well. The upward spread in the bottom surface is most severe since it maintains its boundary layer character for all angles up to !903 and results in long #ame lengths. Although most of the data remained steady, upward spread near the vertical was accelerating with speeds of 30}60 mm/s. 4.2. Theoretical The #ame speeds were computed as a function of angle, orientation, and direction. While they could be computed from Eqs. (2) and (3) together with the #ame length and heat #ux correlations, it was decided to use measured #ame lengths (for upward spread) to compute v directly from Eq. (2). For turbulent upward spread, the procedure was to compute m x from Eq. (20), x from Eq. (19), and q from Eq. (18). The corresponding laminar speeds, for the measured #ame length, will not be reported. They were signi"cantly higher than the turbulent speeds. Downward and nearly horizontal spread on the top surface was computed from the heat #ux and #ame-heated length as given in Fig. 13. The ignition time was computed from Eq. (2b). Properties needed in the computations were estimated from literature values and are given in Table 3. The e!ect of temperatures on speci"c heat was estimated by c"1.5c . Fig. 16 gives the #ame length as measured parallel to the surface and in the direction of spread from the start of pyrolysis. These lengths were estimated from video frames and are not unique when upward acceleration occurred. These values were used to compute the gravity-assisted #ame speeds. The #ame lengths given in Fig. 16 are the total #ame length including the pyrolysis region and should not be confused with the #ame extension or heat transfer length, x !x . Gas phase properties were taken as: "1.2 kg/m, c "1.0 kJ/kg K (air stream), T "298 K,
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309
Fig. 16. Flame length measured parallel to the surface.
"15.3;10\ m/s, Pr"0.73, c "1.4 kJ/kg K (fuel stream). It can be shown that in units of kg, kJ, m, and s the equations needed to predict gravity-assisted #ame spread can be expressed as follows: (m x )"116(cos ) x /H , 2 x "454.3((m x )) /(¸ cos ) , m "(m x )/x , q "m ¸, and q "C B¸(cos ¸) x . * Then we have su$cient information to compute the speed from Eq. (2), v " (x !x )/t . For gravity opposed spread, Eq. (2) can be directly implemented from the #ame heat transfer information given in Fig. 13. The computed results are shown in Fig. 17 and labeled according to the correlations of Ahmad and Faeth (AF) and Ito and Kashiwagi (IK). The predictive results appear to follow the data with reasonable agreement.
5. Discussion Previous studies on the e!ect of inclination on #ame spread have addressed thin materials burning on two sides [3,7,18,19] and thick materials burning on one side
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Fig. 17. Comparison of predicted and measured #ame speeds for the napkin.
[8,19]. All show consistency with the current study of a thin material burning on one side only. They show a critical angle for transition to increasing spread rate for downward spread on the bottom at "!603, and for upward spread on the top at "#603 where the #ame attaches to the surfaces in the boundary layer. From Fig. 17, it is obvious from both theory and experiment that the most serious #ame spread hazard, in terms of speed, is vertical upward spread. Flame spread downward, on either top or bottom, is less than 4 mm/s for all angles except for the bottom horizontal orientation at which it nearly doubles to 9 mm/s. Upward spread on the bottom is generally faster than upward spread on the top. The #ame heat #ux is higher (&50 kW/m) for downward or gravity opposed spread than for upward or gravity-assisted spread with heat #uxes of &10}20 kW/m for angles of 03 to $603. The relatively large #ame heated length for upward spread, roughly 4 cm, causes the higher spread rate for this orientation. Between !753 and 303, GrH was at least 10 VN implying turbulent #ow for all of the gravity-assisted cases. Computed results for the MPET "lm gave similar results to the napkin material. However, the one-dimensional #ame spread theory would not apply to the twodimensional burning as illustrated in Fig. 7b. Although laminar burning conditions did not appear relevant, computations showed that the gravity-assisted cases yielded heat #uxes as high as 50 kW/m and speeds up to 500 mm/s. This suggests that in small #ame tests, such as Bunsen burner ignition tests, the initial #ame speed could be high due to laminar conditions. This will occur before the onset of turbulent #ow. Such results can be misleading and erratic since many sources of disturbance can in#uence the transition to turbulent #ames. Finally, it should be emphasized that the #ame spread speeds reported here apply to comparable conditions of scale and ambient environment. Where accelerating #ames
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might occur for larger scale upward conditions, higher velocities will prevail. Where thermal environments in a developing compartment "re might occur, thermally enhanced speeds will occur.
6. Conclusions This study has shown the e!ect of orientation on #ame spread over thin "lms. It has shown that satisfactory predictive results could be achieved based on general correlations and data in the literature. In the process of executing this analysis, relationships for #ame length were developed for both laminar and turbulent burning of walls. These are consistent with other results in the literature. With respect to safety issues, upward #ame spread is the most serious "re hazard, and upward spread on the bottom of the inclined surface is more hazardous than that corresponding to the top.
Acknowledgements The author is indebted to Sanjeev Gandhi and Sean Crowley for their help in designing the test apparatus and conducting the experiments, to Richard Lyon for his helpful discussions, and to Patricia Cahill for useful discussions and guidance on the #ammability and characteristics of thin "lm acoustic insulation.
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